How to create an Edge extrusion?
I like keeping things procedural, and as much non-destructive as possible.

If you strive for the same goals, then you can use these techniques.

Draw a curve or mesh object in the shape of the cuts you want to make, select it, then Shift-Select the mesh object and enter Edit Mode.

Under Edit Mode select all faces and use the Knife Project modifier to cut the shape into the object.



Now in your mesh mark all edges you want to use as "edge extrusions" as sharp. Ctrl+E > Mark Sharp including the ones you cut and any other you may want.

Then just use a combination of Edge Split modifier > Solifdify modifier > Bevel modifier, and you have an easy to edit object with only the desired edges with indents.